(a)[4]
Determine the exact value of $p$.
(b)[2]
Show, by rearranging, that $q = \sqrt[3]{2 + 18 \ln 3 - q}$.
(c)[2]
Show, using calculations, that $q$ lies between $2.5$ and $3.0$.
(d)[3]
Use an iterative formula based on the equation in (b) to find $q$ correct to $4$ significant figures. Give the outcome of each iteration to $6$ significant figures.